The purpose of this study is to evaluate the safety and efficacy of combining the chemotherapy drug etoposide with a new chemotherapy drug, paclitaxel, in participants with extensive small cell lung cancer. Both agents, etoposide and paclitaxel have been demonstrated to have independent ability to have activity and lead to tumor shrinkage in patients with extensive small cell lung cancer. This combination of drugs have been shown to be safe and tolerable in patients with other tumor types.